Trouble training modified alexnet to compressed sensing task: seeking pointers

I asked about this previously, but now I have cleaned things up and articulated the question better.

I am trying to copy this paper, in which cells are detected in images using alexnet with the last layer modified to output a compressed 1D vector representation of the 2D boolean mask of cell locations in the image.

I’ve implemented the compression/decompression scheme, and now I’m trying to adapt a modified alexnet to the problem of mapping images to vectors. The input images are 1 channel 250x250. The output vectors have length 10000.
Here is the model definition, modified to change output vector length and input number of channels:

class AlexNet(nn.Module):

    def __init__(self,D_out=10000): #modified with D_out
        super(AlexNet, self).__init__()
        self.features = nn.Sequential(
            nn.Conv2d(1, 64, kernel_size=11, stride=4, padding=2), #modified 1channel 
            nn.MaxPool2d(kernel_size=3, stride=2),
            nn.Conv2d(64, 192, kernel_size=5, padding=2),
            nn.MaxPool2d(kernel_size=3, stride=2),
            nn.Conv2d(192, 384, kernel_size=3, padding=1),
            nn.Conv2d(384, 256, kernel_size=3, padding=1),
            nn.Conv2d(256, 256, kernel_size=3, padding=1),
            nn.MaxPool2d(kernel_size=3, stride=2),
        self.classifier = nn.Sequential(
            nn.Linear(256 * 6 * 6, 4096),
            nn.Linear(4096, 4096),
            nn.Linear(4096, D_out), #modified with D_out 

    def forward(self, x):
        x = self.features(x)
        x = x.view(x.size(0), 256 * 6 * 6)
        x = self.classifier(x)
        return x

The training script is

model = AlexNet()
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.01)

k = 30 #size of batch
N = 100 #number epochs

train_loader = DataLoader(train_data, batch_size=k, shuffle=True) #data loader for training
losses = [] #track the losses 

for epoch in range(N): 
    for i,(inputs,targets) in enumerate(train_loader): 
        #prepare batch
        inputs,targets = Variable(inputs), Variable(targets,requires_grad=False)
        #zero gradients 
        #calculate model prediction
        outputs = model(inputs)
        #calculate loss
        loss = criterion(outputs,targets)
        #backpropagate loss 

        # print statistics

(although once I see the loss decreasing on my local machine I’ll move model and variables to gpu on a server)

I have made a set of 1000 training images with 0 to 15 random splotches over the same cat image like this

a training image with random 'cells'

and I have generated the compressed vector representations of the splotch locations (following method 2 from the paper if this matters).

When I attempt to train, the loss does not decrease. Here is the loss versus minibatch iteration:

loss versus minibatch iteration

Another thing I have tried is transferred all unmodified layers from the pretrained alexnet to use as the starting configuration. There is a steep loss decrease in the early iterations followed by the same behavior-- a hovering around 12000 or so.

Any pointers? I have tried multiple learning rates. I tried SGD with momentum. So far I have only run this on my laptop cpu: have I not waited long enough to see a loss decrease? Do I need to wait out multiple epochs? Am I missing something that renders this untrainable? Do I have a bug? Any comments are greatly appreciated!